Trouble combining multiple objects in the same mesh
Blender 2.8 edits all selected objects


  "They show up as being a part of the same mesh,"


A new feature of blender 2.8 is the ability to edit more than one object at once.  When entering edit mode, all selected mesh objects toggle into edit mode. 

Going by the outliner in screenshot this is the case.

There is no need to separate them again.  Separating adds the newly separated object in object mode, so it appears to work, but is probably unnecessary  

To edit one at a time, toggle out of edit mode, select only one object and toggle back in.